arXiv research

New regularization method corrects over-shrinkage in small data regression.

Study on negative Sasakian structures on specific 5-manifolds.

The hyperbolization process affects the structure of manifolds.

Study optimal ridge regularization for out-of-distribution prediction.

nUDEs use neural networks to model biology without negative values.

Local regularization fails in transductive learning for some multiclass problems.

Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance on a variety of computer vision tasks, particularly visual classification problems, where new algorithms reported to achieve or even surpass the human performance. In this paper, we examine whether CNNs are capable of learning the semantics…

Bayesian Markowitz portfolio problem shows entropy regularization is ineffective.

Study proves solenoidal injectivity for tensor fields on curved manifolds with low regularity.

Regularized training of an autoencoder typically results in hidden unit biases that take on large negative values. We show that negative biases are a natural result of using a hidden layer whose responsibility is to both represent the input data and act as a selection mechanism that ensures sparsity of the representati…

The existence of essential closed surfaces surfaces is proven for finite coverings of 3-manifolds that are triangulated by finitely many topological ideal tetrahedra and admit a regular, negatively curved, ideal structure.

Inspired by the idea of Colding-Minicozzi in [CM1], we define (mean curvature flow) entropy for submanifolds in a general ambient Riemannian manifold. In particular, this entropy is equivalent to area growth of a closed submanifold in a closed ambient manifold with non-negative Ricci curvature. Moreover, this entropy i…

An embedded cubic graph consisting of segments of geodesics such that the angles at any vertex are equal to $2π/3$ is a closed local minimal net. This net is regular if all segments of geodesics are equal. The problem of classification of closed local minimal nets on surfaces of constant negative curvature has been for…

New method for comparing different mass measures on tree structures using entropy partial transport.

Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a paradigm according to which sparsity-promoting regularization is regarded as a n…

Smooth solutions found for a specific type of Yamabe problem.

Study shows negatively curved manifolds' spherical volume equals minimal surface area.

Positive mass theorem for asymptotically flat manifolds with non-negative distributional scalar curvature

Paper reformulates UOT as non-negative penalized linear regression for efficient algorithms.

SOS programming verifies MTW tensor non-negativity for optimal transport maps.

Recently, self-normalizing neural networks (SNNs) have been proposed with the intention to avoid batch or weight normalization. The key step in SNNs is to properly scale the exponential linear unit (referred to as SELU) to inherently incorporate normalization based on central limit theory. SELU is a monotonically incre…

FTRL algorithm with negative entropy regularizer achieves best-of-three-world results for linear bandits.

New scalable algorithm for non-negative linear regression with entropy-regularized OT loss.

This work shows dimension regularization can replace skip-gram negative sampling for graph embeddings, improving efficiency and performance.

New method improves source separation using NMF and adversarial learning.

Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as it is not a regular statistical model, resulting that theoretical optimization me…

A conventional wisdom in statistical learning is that large models require strong regularization to prevent overfitting. Here we show that this rule can be violated by linear regression in the underdetermined $n\ll p$ situation under realistic conditions. Using simulations and real-life high-dimensional data sets, we d…

In this paper we study a particular version of the Hermitian curvature flow (HCF) over a compact complex Hermitian manifold $(M,g,J)$. We prove that if the initial metric has Griffiths positive (non-negative) Chern curvature $Ω$, then this property is preserved along the flow. On a manifold with Griffiths non-negative …

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed …

Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix construction, low-dimensional embedding, and K-Means clustering as post processing), whi…

Paper introduces negative margin loss for better few-shot classification accuracy.

New class of complex manifolds defined, properties studied.

We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space $W^{2, n/2}_{loc}$ for manifolds of dimension less than or equal to $7$ or spin-manifolds of any dimension. More generally, we give a (negative) lower bound on the ADM mass of metrics for which the scalar curvat…

Study interpolating estimators for causal learning from observational data.

A new method for PU learning improves classification error on CIFAR-10.

We consider flows, called $W^{\rm u}$ flows, whose orbits are the unstable manifolds of a codimension one Anosov flow. Under some regularity assumptions, we give a short proof of the strong mixing property of $W^{\rm u}$ flows and we show that $W^{\rm u}$ flows have purely absolutely continuous spectrum in the orthocom…

The paper proves finite topological type theorems for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume.

We revisit skip-gram negative sampling (SGNS), one of the most popular neural-network based approaches to learning distributed word representation. We first point out the ambiguity issue undermining the SGNS model, in the sense that the word vectors can be entirely distorted without changing the objective value. To res…

Study properties of solutions with singularities in the negative cone.

The study addresses negative transfer in multi-output Gaussian processes by proposing latent structures.

In this paper, complex Hessian equation over Kähler manifold was studied. Under the condition that the underline Kähler manifold has non-negative holomorphic bisectional curvature, the existence and regularity of the solution was proved.

In this paper, we compare Ollivier Ricci curvature and Bakry-Émery curvature notions on combinatorial graphs and discuss connections to various types of Ricci flatness. We show that non-negativity of Ollivier Ricci curvature implies non-negativity of Bakry-Émery curvature under triangle-freeness and an additional in-de…

Low regularity spacetimes split into simpler structures.

ReLU networks implicitly favor low-rank solutions, but not as strongly as linear networks.

The fused lasso penalizes a loss function by the $L_1$ norm for both the regression coefficients and their successive differences to encourage sparsity of both. In this paper, we propose a Bayesian generalized fused lasso modeling based on a normal-exponential-gamma (NEG) prior distribution. The NEG prior is assumed in…

New approach to portfolio optimization shows entropy regularization is ineffective.

A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. The score matching method of Hyvärinen [2005] …

We prove a local boundary regularity result for the complete Kahler-Einstein metrics of negative Ricci curvature near strictly pseudoconvex boundary point. We also study the asymptotic behaviour of their holomorphic bisectional curvatures near such points.